{
  "abstract": "When multiple differential cross-section measurements are extracted from a common event sample, the same events contribute simultaneously to multiple distributions. This event-sharing structure imposes exact linear constraints among the bin counts, reducing the effective dimensionality of the measurement below the total number of bins. Since the covariance matrix obeys these inter-distribution constraints, it contains a rank deficiency. While limited numerical precision may inadvertently restore invertibility, the $χ^{2}$ contributions along constrained dimensions will be arbitrary, yielding unphysically inflated $χ^{2}$ values in global goodness-of-fit tests. We present the range-projected $χ^{2}$, a test statistic that restricts the goodness-of-fit test to the subspace carrying independent statistical information, yielding a $χ^{2}$ with $N_\\text{bins} - N_\\text{null}$ degrees of freedom, where $N_\\text{null}$ is the number of independent constraints. We show that this rank deficiency is a predictable consequence of the event-sharing structure, and that $N_\\text{null}$ decomposes into a structural contribution determined a priori from the binning geometry and a kinematic contribution that depends on the phase-space occupancy. The method is validated with an analytical toy model and a simulated neutrino--argon cross-section measurement including unfolding and multi-source systematic uncertainties.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24796",
  "author_total": 5,
  "authors": [
    {
      "name": "Francisco Martinez Lopez"
    },
    {
      "name": "London Cooper-Troendle"
    },
    {
      "name": "Steven Gardiner"
    },
    {
      "name": "Patrick Green"
    },
    {
      "name": "Tanaz Mohayai"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/48w32fyb6c92t.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24796",
  "fulltext_url": null,
  "id": "48w32fyb6c92t",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24796",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "hep-ex"
    ],
    [
      "arxiv",
      "physics.data-an"
    ],
    [
      "openalex",
      "3106|Neutrino Physics Research"
    ]
  ],
  "openalex": "W7214005848",
  "pdf_url": "https://arxiv.org/pdf/2609.24796",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/48w32fyb6c92t.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:19Z",
      "native_id": "2609.24796",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24796"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.data-an",
      "subfield": "computational"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-ex",
      "subfield": "high-energy"
    }
  ],
  "title": "Goodness-of-fit for multi-distribution neutrino cross-section measurements with shared events",
  "title_text": "Goodness-of-fit for multi-distribution neutrino cross-section measurements with shared events",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:19Z",
  "url": "https://research.draconitic.com/paper/48w32fyb6c92t",
  "venue": "arXiv",
  "versions": []
}